The following line passes through point $(6, 10)$ : $y = \dfrac{19}{8} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(6, 10)$ into the equation gives: $10 = \dfrac{19}{8} \cdot 6 + b$ $10 = \dfrac{57}{4} + b$ $b = 10 - \dfrac{57}{4}$ $b = -\dfrac{17}{4}$ Plugging in $-\dfrac{17}{4}$ for $b$, we get $y = \dfrac{19}{8} x - \dfrac{17}{4}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(6, 10)$